PSG has now won the prestigious trophy on fourteen different occasions.
Paris Saint-Germain needed a stoppage-time equaliser followed by a successful spot-kick decider to overcome their arch-rivals in the Gulf and capture a fourth straight French Super Cup title.
The European champions appeared to be coasting towards a straightforward triumph in the showdown featuring the French league winners and the French Cup holders after the French winger opened the scoring in the opening stages.
However, the southern French side fired two times in the closing moments to take a surprise lead. Initially, the English forward converted from the penalty spot, before Willian Pacho inadvertently turned the ball into his own net for an own goal.
In a remarkable turn of fortune, the Portuguese striker grabbed a crucial leveler in the final moments to send the contest into a penalty shootout. The Parisian shot-stopper Chevalier then stood as the key figure, stopping crucial attempts from Matt O'Riley and Traore.
In the shootout, Goncalo Ramos, Vitinha, the full-back, and the young talent all converted successfully for PSG to complete a convincing shootout win.
Now 14-time champions Paris Saint-Germain, who met last season's Ligue 1 second-placed team Marseille after achieving a league and cup double, have now lifted this competition for the twelfth time in the past thirteen seasons.
